The Abiogenesis Timescale (2503.18217v1)

Abstract: If two physical timescales are independent, i.e. they depend on different physics, then (statistically) there is no reason to believe that their values should be equal, even to an order of magnitude. The timescale for abiogenesis $\tau_{AB}$, which depends primarily on prebiotic-chemistry, is expected to be independent of the planetary habitability timescale $\tau_{Hab}$, which depends primarily on the sun and therefore on nuclear forces and gravity. Therefore, we expect that either $\tau_{AB} \ll \tau_{Hab}$ or $\tau_{AB} \gg \tau_{Hab}$. The correct inequality is universal and a single example should suffice to resolve this binary choice. Here I argue that, contrary to a well known anthropic selection effect, our existence (which entails life on Earth) can be considered evidence that the correct choice is the former. A Bayesian analysis, taking into account that our existence is old evidence, implies that the probability of the hypothesis $\tau_{AB} \ll \tau_{Hab}$ is > 0.91, assuming equal priors. The Bayes factor, which depends only on the evidence, is > 10 and suggests strong to decisive support for the short abiogenesis timescale hypothesis, according to the Jeffreys interpretation.

• The paper reinterprets the anthropic argument by evaluating life’s emergence using counterfactual Bayesian likelihoods prior to abiogenesis.
• It demonstrates that if abiogenesis is rapid (T₍AB₎ ≪ T₍Hab₎), the posterior probability exceeds 90% with a Bayes Factor over 10 favoring the 'AB easy' hypothesis.
• The framework offers a practical model to refine astrobiological search strategies and computational studies in exoplanet biosignature detection.

This paper (2503.18217) addresses a long-standing argument in astrobiology regarding whether the existence of life on Earth (LoE) provides evidence that abiogenesis (the origin of life) is likely to occur quickly on other Earth-like planets. The traditional argument, based on an anthropic selection effect, suggests that since we can only observe life on a planet where it did arise, our existence is neutral evidence about the general probability of abiogenesis.

The core of the paper's counter-argument lies in the treatment of "old evidence" within a Bayesian framework. The author argues that when applying Bayes' theorem to old evidence (like LoE or the specific outcomes in the examples provided), the likelihoods – the probability of observing the evidence given a hypothesis, $P(\text{Evidence}|\text{Hypothesis})$ – should be evaluated counterfactually, prior to the evidence actually occurring.

The paper illustrates this point with several analogies:

1. Coin Flips: Observing three heads in a row from a coin. A naive application of Bayes with old evidence might set $$P(3\text{heads}|\text{fair})=P(3\text{heads}|\text{not fair})=1$$. The paper argues the likelihoods should be evaluated before the flips, where $P(3\text{heads}|\text{fair}) = (1/2)^3$ and $P(3\text{heads}|\text{not fair})$ would depend on the distribution of bias for unfair coins.
2. Urn Problem: Drawing marble #7 from an urn, knowing the urn is either one with 10 marbles (1-10) or one with 1,000,000 marbles (1-1,000,000). Naively, the likelihoods might be seen as 1. The paper argues they should be evaluated prior to the draw: $P(\#7|\text{10 marbles}) = 1/10$ and $P(\#7|\text{1,000,000 marbles}) = 1/1,000,000$. This leads to a posterior probability strongly favoring the 10-marble urn.
3. Conception Analogy: Your existence as evidence for whether human conception is generally "easy" or "hard" (e.g., with or without contraception). The paper argues likelihoods should be the probability of conception prior to it happening, given the 'easy' or 'hard' hypothesis, rather than 1 because you already exist.

Applying this "old evidence" approach to abiogenesis, the paper defines two hypotheses based on an independent-timescale argument:

• Hypothesis "AB easy": The timescale for abiogenesis ($T_{AB}$, dependent on prebiotic chemistry) is much less than the planetary habitability timescale ($T_{Hab}$, dependent on stellar evolution, gravity, nuclear physics). $T_{AB} \ll T_{Hab}$.
• Hypothesis "AB hard": $T_{AB} \gg T_{Hab}$.

The independent-timescale argument suggests that because $T_{AB}$ and $T_{Hab}$ depend on fundamentally different physics, their values are unlikely to be coincidentally similar. The paper provides examples comparing radioactive decay half-lives (nuclear physics) with astronomical periods (gravity) to support this statistical argument, showing that random comparisons of independent timescales are rarely within an order of magnitude of each other. This bifurcation into $T_{AB} \ll T_{Hab}$ or $T_{AB} \gg T_{Hab}$ simplifies the hypothesis space.

The paper then sets up the Bayesian calculation for the posterior probability of "AB easy" given the evidence of LoE:

$$P(\text{AB easy}|\text{LoE}) = \frac{P(\text{LoE prior to AB}|\text{AB easy})P(\text{AB easy})}{P(\text{LoE prior to AB}|\text{AB easy})P(\text{AB easy}) + P(\text{LoE prior to AB}|\text{AB hard})P(\text{AB hard})}$$

The crucial step is evaluating the likelihoods prior to abiogenesis. The paper argues:

• $P(\text{LoE prior to AB}|\text{AB easy})$: If abiogenesis is easy and fast ($T_{AB} \ll T_{Hab}$), the probability of life arising within the habitable window is high, approximated as ~1.
• $P(\text{LoE prior to AB}|\text{AB hard})$: If abiogenesis is hard and slow ($T_{AB} \gg T_{Hab}$), the probability of life arising within the habitable window (which is much shorter than $T_{AB}$) is very low, represented by $\epsilon$, where $\epsilon \ll 1$. The paper uses $\epsilon < 1/10$.

With these likelihoods ($1$ and $\epsilon$) and assuming equal prior probabilities for "AB easy" and "AB hard" ($P(\text{AB easy}) = P(\text{AB hard}) = 0.5$), the posterior probability becomes:

$$P(\text{AB easy}|\text{LoE}) = \frac{1 \times 0.5}{1 \times 0.5 + \epsilon \times 0.5} = \frac{0.5}{0.5(1+\epsilon)} = \frac{1}{1+\epsilon}$$

Since $\epsilon < 1/10$, $1+\epsilon < 1.1$, so $P(\text{AB easy}|\text{LoE}) > 1/1.1 \approx 0.91$.

Alternatively, the Bayes Factor ($BF$) is calculated as the ratio of the likelihoods: $$BF = \frac{P(\text{LoE prior to AB}|\text{AB easy})}{P(\text{LoE prior to AB}|\text{AB hard})} = \frac{1}{\epsilon}$$. Given $\epsilon < 1/10$, the Bayes Factor is $> 10$. According to the Jeffreys interpretation, a Bayes Factor greater than 10 provides "strong to decisive" evidence in favor of the hypothesis "AB easy" ($T_{AB} \ll T_{Hab}$).

Practical Implications and Implementation Considerations:

While this is a theoretical astrobiology paper, its implications are significant for guiding future research and interpretation in fields like exoplanet studies and the search for extraterrestrial life.

• Informing Astrobiological Search Strategies: The conclusion that abiogenesis is likely easy/fast suggests that if suitable conditions exist on an exoplanet, life might arise relatively early in the planet's history and within its habitable lifetime. This could influence where scientists focus their search efforts (e.g., looking for biosignatures on relatively young, but stable, planets in habitable zones).
• Interpreting Future Data: Discovering biosignatures on exoplanets would serve as new evidence. The framework presented could be adapted to update the probabilities based on such discoveries. If life is found on a planet where $T_{AB}$ is short relative to $T_{Hab}$, it would further strengthen this conclusion.
• Computational Models: The core of the paper is a Bayesian calculation. Implementing this involves:
  • Defining the hypotheses: Representing "AB easy" and "AB hard" based on the $T_{AB}$ vs $T_{Hab}$ relationship.
  • Assigning priors: The paper assumes equal priors, but future work could explore the sensitivity of the results to different prior distributions for $T_{AB}$ and $T_{Hab}$ or the probability of each hypothesis.
  • Quantifying likelihoods: The main challenge in a more detailed implementation would be assigning more precise, data-driven values to $P(\text{LoE prior to AB}|\text{H})$. This would require input from prebiotic chemistry models and planetary science to estimate the probability of abiogenesis arising by time $t$ on a generic Earth-like planet under different scenarios. The parameter $\epsilon$ needs a more robust justification than just "< 1/10".
  • Performing Bayesian update: Implementing the formula $$P(\text{H}|\text{E}) = \frac{P(\text{E}|\text{H})P(\text{H})}{P(\text{E})}$$ using the "prior to evidence" likelihoods. This is standard Bayesian inference which can be implemented using basic probability calculations or probabilistic programming libraries (though overkill for this simple case).
  • Calculating Bayes Factors: Simple ratio calculation of likelihoods.

prior_easy = 0.5 prior_hard = 0.5 epsilon = 0.05 likelihood_easy = 1.0 likelihood_hard = epsilon marginal_likelihood = likelihood_easy * prior_easy + likelihood_hard * prior_hard posterior_easy = (likelihood_easy * prior_easy) / marginal_likelihood bayes_factor = likelihood_easy / likelihood_hard print(f"Assumed epsilon: {epsilon}") print(f"Posterior probability P(AB easy | LoE): {posterior_easy:.4f}") print(f"Bayes Factor (BF): {bayes_factor:.2f}") epsilon_small = 0.01 likelihood_hard_small = epsilon_small marginal_likelihood_small = likelihood_easy * prior_easy + likelihood_hard_small * prior_hard posterior_easy_small = (likelihood_easy * prior_easy) / marginal_likelihood_small bayes_factor_small = likelihood_easy / likelihood_hard_small print(f"\nAssumed epsilon: {epsilon_small}") print(f"Posterior probability P(AB easy | LoE): {posterior_easy_small:.4f}") print(f"Bayes Factor (BF): {bayes_factor_small:.2f}")

• Limitations: The analysis depends critically on the "old evidence" interpretation of Bayesian inference, which is a topic of philosophical debate. It also relies on the independent-timescale argument accurately capturing the relationship between $T_{AB}$ and $T_{Hab}$. The specific value of $\epsilon$ (the probability of life arising by chance in the 'hard' scenario) is not rigorously derived from empirical data but assumed to be small. Real-world applications would need to grapple with these uncertainties. The assumption of equal priors is a common starting point but may not reflect actual domain knowledge if available.

In summary, the paper provides a theoretical framework, based on a specific interpretation of Bayesian probability and a timescale argument, to argue that our existence suggests abiogenesis is likely a relatively rapid process on suitable planets. While not offering direct code for deployment, the structure of the argument provides a model for how to apply Bayesian reasoning to observational data in astrobiology, highlighting the importance of carefully defining likelihoods, especially when dealing with unique, pre-existing evidence like the origin of life on Earth.